In discrete multitone (DMT) transceivers, a cyclic prefix is inserted between transmitted symbols such that the linear convolution of the data and the channel impulse response becomes a circular one corresponding to term-by-term product in the frequency domain. If the cyclic prefix length is longer than that of the channel impulse response it avoids the intersymbol interference (ISI). To reduce the inefficiency due to the use of a long cyclic prefix, the use of a time domain equalizer (TEQ) to shorten the effective channel impulse response has been the most popular equalization approach. In this paper, we pose the TEQ problem completely in the frequency domain by defining a cost function in the frequency domain and derive a new learning algorithm for the TEQ training. In the echo-cancellation based DMT system, the TEQ can also be used to jointly shorten the echo response thus can effectively reduce the complexity of the echo-canceller. We define a composite squared cost function to account for these two shortening purposes and derive a new joint shortening algorithm for the TEQ which can effectively reduce the lengths of channel and echo impulse responses simultaneously.